Basic Math Examples

$\frac{2}{3} + \frac{3}{4} \div (\frac{7}{10} - \frac{1}{5}) \cdot \frac{2}{5}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} + \frac{3}{4} \div (\frac{7}{10} - \frac{1}{5} \cdot \frac{2}{2}) \cdot \frac{2}{5}$

Step 1.1.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.2.1

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{2}{3} + \frac{3}{4} \div (\frac{7}{10} - \frac{2}{5 \cdot 2}) \cdot \frac{2}{5}$

Step 1.1.2.2

Multiply $5$ by $2$ .

$\frac{2}{3} + \frac{3}{4} \div (\frac{7}{10} - \frac{2}{10}) \cdot \frac{2}{5}$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{2}{3} + \frac{3}{4} \div \frac{7 - 2}{10} \cdot \frac{2}{5}$

Step 1.1.4

Subtract $2$ from $7$ .

$\frac{2}{3} + \frac{3}{4} \div \frac{5}{10} \cdot \frac{2}{5}$

Step 1.1.5

Cancel the common factor of $5$ and $10$ .

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Step 1.1.5.1

Factor $5$ out of $5$ .

$\frac{2}{3} + \frac{3}{4} \div \frac{5 (1)}{10} \cdot \frac{2}{5}$

Step 1.1.5.2

Cancel the common factors.

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Step 1.1.5.2.1

Factor $5$ out of $10$ .

$\frac{2}{3} + \frac{3}{4} \div \frac{5 \cdot 1}{5 \cdot 2} \cdot \frac{2}{5}$

Step 1.1.5.2.2

Cancel the common factor.

$\frac{2}{3} + \frac{3}{4} \div \frac{5 \cdot 1}{5 \cdot 2} \cdot \frac{2}{5}$

Step 1.1.5.2.3

Rewrite the expression.

$\frac{2}{3} + \frac{3}{4} \div \frac{1}{2} \cdot \frac{2}{5}$

Step 1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{3} + \frac{3}{4} \cdot 2 \cdot \frac{2}{5}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$\frac{2}{3} + \frac{3}{2 (2)} \cdot 2 \cdot \frac{2}{5}$

Step 1.3.2

Cancel the common factor.

$\frac{2}{3} + \frac{3}{2 \cdot 2} \cdot 2 \cdot \frac{2}{5}$

Step 1.3.3

Rewrite the expression.

$\frac{2}{3} + \frac{3}{2} \cdot \frac{2}{5}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$\frac{2}{3} + \frac{3}{2} \cdot \frac{2}{5}$

Step 1.4.2

Rewrite the expression.

$\frac{2}{3} + 3 \cdot \frac{1}{5}$

Step 1.5

Combine $3$ and $\frac{1}{5}$ .

$\frac{2}{3} + \frac{3}{5}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5}$

Step 3

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 5}{3 \cdot 5} + \frac{3}{5} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $5$ .

$\frac{2 \cdot 5}{15} + \frac{3}{5} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{5 \cdot 3}$

Step 4.4

Multiply $5$ by $3$ .

$\frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 3 \cdot 3}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{10 + 3 \cdot 3}{15}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{10 + 9}{15}$

Step 6.3

Add $10$ and $9$ .

$\frac{19}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{15}$

Decimal Form:

$1.2\overline{6}$

Mixed Number Form:

$1 \frac{4}{15}$